200 research outputs found
Optimal Equivocation in Secrecy Systems a Special Case of Distortion-based Characterization
Recent work characterizing the optimal performance of secrecy systems has
made use of a distortion-like metric for partial secrecy as a replacement for
the more traditional metric of equivocation. In this work we use the log-loss
function to show that the optimal performance limits characterized by
equivocation are, in fact, special cases of distortion-based counterparts. This
observation illuminates why equivocation doesn't tell the whole story of
secrecy. It also justifies the causal-disclosure framework for secrecy (past
source symbols and actions revealed to the eavesdropper).Comment: Invited to ITA 2013, 3 pages, no figures, using IEEEtran.cl
A Universal Scheme for Wyner–Ziv Coding of Discrete Sources
We consider the Wyner–Ziv (WZ) problem of lossy compression where the decompressor observes a noisy version of the source, whose statistics are unknown. A new family of WZ coding algorithms is proposed and their universal optimality is proven. Compression consists of sliding-window processing followed by Lempel–Ziv (LZ) compression, while the decompressor is based on a modification of the discrete universal denoiser (DUDE) algorithm to take advantage of side information. The new algorithms not only universally attain the fundamental limits, but also suggest a paradigm for practical WZ coding. The effectiveness of our approach is illustrated with experiments on binary images, and English text using a low complexity algorithm motivated by our class of universally optimal WZ codes
Empirical processes, typical sequences and coordinated actions in standard Borel spaces
This paper proposes a new notion of typical sequences on a wide class of
abstract alphabets (so-called standard Borel spaces), which is based on
approximations of memoryless sources by empirical distributions uniformly over
a class of measurable "test functions." In the finite-alphabet case, we can
take all uniformly bounded functions and recover the usual notion of strong
typicality (or typicality under the total variation distance). For a general
alphabet, however, this function class turns out to be too large, and must be
restricted. With this in mind, we define typicality with respect to any
Glivenko-Cantelli function class (i.e., a function class that admits a Uniform
Law of Large Numbers) and demonstrate its power by giving simple derivations of
the fundamental limits on the achievable rates in several source coding
scenarios, in which the relevant operational criteria pertain to reproducing
empirical averages of a general-alphabet stationary memoryless source with
respect to a suitable function class.Comment: 14 pages, 3 pdf figures; accepted to IEEE Transactions on Information
Theor
Wyner-Ziv coding based on TCQ and LDPC codes and extensions to multiterminal source coding
Driven by a host of emerging applications (e.g., sensor networks and wireless
video), distributed source coding (i.e., Slepian-Wolf coding, Wyner-Ziv coding and
various other forms of multiterminal source coding), has recently become a very active
research area.
In this thesis, we first design a practical coding scheme for the quadratic Gaussian
Wyner-Ziv problem, because in this special case, no rate loss is suffered due to
the unavailability of the side information at the encoder. In order to approach the
Wyner-Ziv distortion limit D??W Z(R), the trellis coded quantization (TCQ) technique
is employed to quantize the source X, and irregular LDPC code is used to implement
Slepian-Wolf coding of the quantized source input Q(X) given the side information
Y at the decoder. An optimal non-linear estimator is devised at the joint decoder
to compute the conditional mean of the source X given the dequantized version of
Q(X) and the side information Y . Assuming ideal Slepian-Wolf coding, our scheme
performs only 0.2 dB away from the Wyner-Ziv limit D??W Z(R) at high rate, which
mirrors the performance of entropy-coded TCQ in classic source coding. Practical
designs perform 0.83 dB away from D??W Z(R) at medium rates. With 2-D trellis-coded
vector quantization, the performance gap to D??W Z(R) is only 0.66 dB at 1.0 b/s and
0.47 dB at 3.3 b/s.
We then extend the proposed Wyner-Ziv coding scheme to the quadratic Gaussian
multiterminal source coding problem with two encoders. Both direct and indirect
settings of multiterminal source coding are considered. An asymmetric code design
containing one classical source coding component and one Wyner-Ziv coding component
is first introduced and shown to be able to approach the corner points on the
theoretically achievable limits in both settings. To approach any point on the theoretically
achievable limits, a second approach based on source splitting is then described.
One classical source coding component, two Wyner-Ziv coding components, and a
linear estimator are employed in this design. Proofs are provided to show the achievability
of any point on the theoretical limits in both settings by assuming that both
the source coding and the Wyner-Ziv coding components are optimal. The performance
of practical schemes is only 0.15 b/s away from the theoretical limits for the
asymmetric approach, and up to 0.30 b/s away from the limits for the source splitting
approach
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